First slide

Simple hormonic motion

Question

In the figure all springs are identical having spring constant K and mass m each. The block has also mass m. The frequency of oscillation of the block is

Moderate

A

$\frac{1}{2 π} \sqrt{\frac{3 k}{m}}$
B

$\frac{1}{2 π} \sqrt{\frac{3 k}{2 m}}$
C

$2 π \sqrt{\frac{3 m}{2 k}}$
D

$\frac{1}{π} \sqrt{\frac{3 m}{k}}$

Solution

If a spring has $m_{s}$ then
$f = \frac{1}{2 π} \sqrt{\frac{k}{m + \frac{m_{s}}{3}}}$
Spring constant = 3k.
$f = \frac{1}{2 π} \sqrt{\frac{3 k}{m + \frac{3 m}{3}}} = \frac{1}{2 π} \sqrt{\frac{3 k}{2 m}}$

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